PROBLEM B.73* (Continued)
Simplifying
33 3
0.12533( ) ( ) 0.5( ) 0
xy z
33
zx
and then
33
3
( ) [ 0.12533 (0.5)(0.06522)]( )
0.15794( )
yx
x
33
yz
33 3
( ) 9.7 ( ) 99.0 ( ) 86.3
xy z
333
xyz
PROBLEM B.74*
For the component described in Problems 9.148 and 9.170,
determine (a) the principal mass moments of inertia at the origin,
(b) the principal axes of inertia at the origin. Sketch the body and
show the orientation of the principal axes of inertia relative to the
x, y, and z axes.
1113
() () ( )() 0
zx x yz y z z
II IK
PROBLEM B.74* (Continued)
Substituting
11
(0.096768)( ) (0.41933 0.22583)( ) 0
xy
22
1
( ) 2[0.50009( ) ] 1
xx
or 1
( ) 0.81645
x
and 11
( ) ( ) 0.40830
yz
xxxyyzxz
2222
() ( )() () 0
xy x y y yz z
IIKI
Substituting
x
and then Eq. (i) 22
() ()
zy
Now substitute into Eq. (9.57):
z
222
( ) 90.0 ( ) 45.0 ( ) 135.0
xyz
0
0
PROBLEM B.74* (Continued)
3
:K
Begin with Eqs. (9.54
b
) and (9.54
c
):
3333
() ( )() () 0
xy x y y yz z
IIKI
33
xz
Simplifying yields
33 3
() () ()
yz x
Now substitute into Eq. (9.57):
22
3
yz
333
( ) 54.7 ( ) ( ) 125.3
xyz
(
c
)
3
x
33
yz
0
0